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DidOct 17 '12 at 13:47

What I have at my disposition is the definition of a derivative as a limit.
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CarpediemOct 17 '12 at 13:50

I used it as was advised below, but I don't know how to conclude the differentiability in 0. I know we have an expression similar to the limit but I don't know how to continue
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CarpediemOct 17 '12 at 13:59

What you have is not an expression similar to the limit but a precise definition involving a quite definite limit.
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DidOct 17 '12 at 15:21

1 Answer
1

Use the definition of the derivative. It is clear that $f(0)=0$. Note that if $h\ne 0$ then
$$\left|\frac{f(h)-0}{h}\right| \le |h|^{\alpha-1}.$$
Since $\alpha\gt 1$, $|h|^{\alpha-1}\to 0$ as $h\to 0$.